Statistics of Square-tiled Surfaces: Symmetry and Short Loops
Geometric Topology
2019-05-03 v2 Combinatorics
Dynamical Systems
Abstract
Square-tiled surfaces are a class of translation surfaces that are of particular interest in geometry and dynamics because, as covers of the square torus, they share some of its simplicity and structure. In this paper, we study counting problems that result from focusing on properties of the square torus one by one. After drawing insights from experimental evidence, we consider the implications between these properties and their frequency in each stratum of translation surfaces.
Cite
@article{arxiv.1902.08214,
title = {Statistics of Square-tiled Surfaces: Symmetry and Short Loops},
author = {Sunrose T. Shrestha and Jane Wang},
journal= {arXiv preprint arXiv:1902.08214},
year = {2019}
}
Comments
18 pages